Quadratic boost converter for Photovoltaic Micro-Inverter

Ashirvad M#1 and Rupesh K C*2 #PG Student, EEE Dept., Siddaganga Institute of Technology, Karnataka, India

* Assistant Professor, EEE Dept., Siddaganga Institute of Technology, Karnataka, India

Abstract A Quadratic boost converter for Dual-stage photovoltaic micro-inverter with sliding-mode control is discussed in this paper. The proposed topology is a dual-stage structure with a quadratic boost converter in the DC-DC stage and a full-bridge inverter in the DC-AC stage. The quadratic boost uses a sliding-mode current controller and a proportional-integral (PI) compensator regulating the output voltage. The full-bridge inverter uses sinusoidal pulse-width modulation[SPWM] technique for DC to AC inversion. Each converter overall system is discussed and simulation result are presented.

Index TermsQuadratic boost converter, Sliding-mode control, photovoltaic panel, Dual-stage micro-inverter.

I. INTRODUCTION In the market of solar inverter demand has increased

dramatically in the last few years due to liberalization of electricity market in many countries and establishing government policies for purchasing electricity produced by the means of renewable energy. Grid connected inverter supply either 110 V or 220 V at 60 Hz or 50 Hz respectively. The single-phase or three-phase structures are classified into four categories: micro, string, multi string and central inverters. Micro-inverter is single-phase DC-AC converter operated with an input range of 20 Vdc to 50 Vdc and delivering an active power not more than 500 W. String inverter is also single-phase converter structure with an input of 40 Vdc-200 Vdc and an output power ranges between 1KW to 3 KW. Multi-string inverter can be single-phase or three-phase structure with input of 50 Vdc and 600 Vdc and output between 3 KW to 20 KW. A central inverter is always three-phase DC-AC converter supply a power more than 20 KW for an input voltage in the range of 200 Vdc-300Vdc.

The present trend is focused on multi-string and module-oriented technology in medium and low power applications [1]. The photovoltaic-module oriented technology is to install the system with a simple mechanical assembly and is easier to connect to a grid. The module oriented inverter is classified as single-stage, dual-stage and multi-stage, considering the number of power processing stages connected in cascade with in the inverter. A recent compression identifies the dual-stage topologies with DC-DC stage and DC-AC stage as the most competitive solution in module oriented converter. Grid-connected solar micro-inverter basically of two stages: first stage operating at high frequency to step up the panel voltage

upto 400 Vdc and second stage operating at grid frequency to transform dc to ac and subsequent connection to the public utility. These inverters are operated at the lowest power range; their weight and volume are susceptible of minimization in view of a mechanical integration in the back side of the same photovoltaic (PV) panel [2].

In this approach, the first step is either to minimize or remove of the high frequency transformer, which is a common element in commercial micro-inverter. The second step is to define the maximum DC gain required by the step-up voltage converter. Finally potential converter without galvanic isolation that could solve the voltage step-up problem. Therefore a quadratic boost converter has a competitive transformer-less structure to solve the problem of step-up input voltage ranges from 20 Vdc-30 Vdc up to 400 Vdc[2]. This paper discussed a quadratic boost converter which provides a competitive DC-DC structure for module oriented application, also use of the known full bridge inverter in the DC-AC stage [1]. A stable and reliable operation can be obtained using the sliding mode control approach, since control with simplicity and robustness, also taking the advantage of both converters is variable structure system. In case of DC-DC converter based on PWM control, the high-gain can leads to modulator saturation since the duty cycle near to unsafe operating region; thus sliding mode control approach is more reliable choice. In the case of the DC-AC converter, it is known the capacity of the sliding-mode approach to obtain instantaneous time-varying reference tracking, which is different from linear control approaches.

The possible existence of high-frequency oscillations in the control signal (chattering) is a sensitive drawback of the sliding-mode control leading to different solutions [3]. In this sense, the hysteresis comparator offers an alternative solution in real time implementation of power converters, keeping a regular behavior in the controlled states [4] and eliminating the effect of the non-modeling dynamics in the commutation events. However, the hysteresis band leads to a non-ideal sliding-mode introducing a frequency variation that should also be restricted. To conclude, the hysteresis band should be small enough to reduce the high-frequency component and wide enough to avoid the influence of spurious noise and transients.

II. OVERALL SYSTEM DESCRIPTION.

Fig. 1. Block diagram of a two-stage photovoltaic micro

The micro-inverter as shown in Fig. 1 composed of a power block and a control block. The power block hasDC converter and a DC-AC converter connected in cascade. The control block has a dedicated controller for each power stage and a maximum power point tracker (MPPT). The control of the DC-DC stage regulates an output voltage to a value between 15 to 30 times higher than the one of input voltage. The control of the DC-AC stage shapes a sinusoidal voltage waveform.

The micro-inverter has a quadratic boost converter in the DC-DC stage and a full-bridge inverter in the DCThe quadratic boost operates in continuous conduction mode (CCM) along with its overall operational range, while the fullbridge inverter uses bipolar commutation. The quadratic boost is controlled to regulate a DC voltage bus with a level higher than the peak voltage of the utility in order to guarantee the adequate direction on the power flow. Meanwhile, the fullbridge inverter employs SPWM technique is used to control the inverter as it can be directly controlled the inverter output voltage and frequency according to the sine Sinusoidal pulse width modulation (SPWM) is widely used in power electronics to digitize the power so that a sequence of voltage pulses can be generated by the on and off of the power switches.

III. DC-DC STAGE: QUADRATIC BOOST CONVERTER

The quadratic boost converter shown in Fig. 2 results from the generalized cascaded boost topologies with a single switch introduced in [5]. This converter allows covering gain ranges which are not available with the single boost converter even though, cubic boost converter gives more gain; efficiency is low compared to quadratic boost converter [2]. Considering variable quadratic boost converter structure, with an input gating signal u, the non-linear equation for the system are given in eq. 1(a)-(d)

OVERALL SYSTEM DESCRIPTION.

stage photovoltaic micro-inverter

inverter as shown in Fig. 1 composed of a power block and a control block. The power block has a DC-

AC converter connected in cascade. The control block has a dedicated controller for each power stage and a maximum power point tracker (MPPT). The

DC stage regulates an output voltage to a 0 times higher than the one of input

AC stage shapes a sinusoidal

inverter has a quadratic boost converter in the bridge inverter in the DC-AC stage. ates in continuous conduction mode

(CCM) along with its overall operational range, while the full-bridge inverter uses bipolar commutation. The quadratic boost is controlled to regulate a DC voltage bus with a level higher

ity in order to guarantee the adequate direction on the power flow. Meanwhile, the full-

technique is used to control the inverter as it can be directly controlled the inverter output voltage and frequency according to the sine function [5]. Sinusoidal pulse width modulation (SPWM) is widely used in power electronics to digitize the power so that a sequence of voltage pulses can be generated by the on and off of the power

DC STAGE: QUADRATIC BOOST

ratic boost converter shown in Fig. 2 results from the generalized cascaded boost topologies with a single switch introduced in [5]. This converter allows covering gain ranges which are not available with the single boost converter

converter gives more gain; efficiency is low compared to quadratic boost converter [2]. Considering variable quadratic boost converter structure, with

linear equation for the system

Fig. 2. Quadratic boost converter and control scheme Taking into account that this model corresponds to a

variable structure system controlled by the signal u, we obtain the nonlinear equation system (1).

The sliding-mode control is naturally well suited for the control of variable structure systems. Characterized by switching, power converters are inherently variable structure systems. Therefore, slidingcontrol on power converters. Slidingexcellent large-signal handling capability, which is important for DCDC converters. Since the design of conventional pulse-width modulation (PWM) controllers is smallbased, the converters being controlled operate optimally only for a specific condition and often fail to under large parameter or load variations (i.e., largeoperating condition). By replacing linear PWM controllers with SM (nonlinear) controllers, power converters can achieve better regulation and dynamical performance for a wioperating range [6].As shown in Fig. 2, if the PI compensator loop is annulled; an indirect slidingused to stabilize the output voltage only using a fixed current reference [7]. Considering the current reference as the timevarying function IL1ref, we obtain the sliding surface expression as in eq. (2).

S(x) = IThe surface S(x) constitutes a current control loop so that in equilibrium (steady-state) iused to regulate the output voltage provided that the current

RL1V

delta

PI

S

TTemp

light_intensity

Quadratic boost converter and control scheme Taking into account that this model corresponds to a

variable structure system controlled by the signal u, we obtain the nonlinear equation system (1).

1 (1.a)

1 (1.b)

1 (1.c)

. 1 (1.d)

mode control is naturally well suited for control of variable structure systems. Characterized by

switching, power converters are inherently variable structure systems. Therefore, sliding-mode is appropriate to apply control on power converters. Sliding-mode control offers

andling capability, which is important DC converters. Since the design of conventional

width modulation (PWM) controllers is small-signal based, the converters being controlled operate optimally only for a specific condition and often fail to perform satisfactorily under large parameter or load variations (i.e., large-signal operating condition). By replacing linear PWM controllers with SM (nonlinear) controllers, power converters can achieve better regulation and dynamical performance for a wider operating range [6].As shown in Fig. 2, if the PI compensator loop is annulled; an indirect sliding-mode current control is used to stabilize the output voltage only using a fixed current reference [7]. Considering the current reference as the time-

, we obtain the sliding surface

S(x) = IL1ref iL1 (2) The surface S(x) constitutes a current control loop so that in

state) iL1 = IL1ref. This surface can also be used to regulate the output voltage provided that the current

D1

C1

RL2D2

C2

Rv1

Rv2

VD3

IL1

VOUT

VgtS

R

Q

Q

vreferPI

VOUT

V

V

RLOAD

reference IL1ref is given by an external loop that processes the output voltage error by means of a compensating network. In our case the compensating network is given by a PI circuit and therefore the switching surface consisting of both inner and outer loops is given as in eq. (4)

!" !"# $ !" !"#%&' (4)

To design the PI compensator, the transfer function (5) of the inner loop is obtained by linearizing the resultant sliding dynamic, this allowing the application of any linear control design method [8].

(5)

Where M=!(" !() !( !)

Sliding mode control law can be implemented by using a hysteresis comparator. With a hysteresis band of 2 between*+, the control law is defined by (6).

,1, . / +0, . 1 +2 (6)

IV. DC-AC STAGE: F ULL- BRIDGE INVERTER The full-bridge is a converter topology, which is commonly used in voltage source inverters (VSI), current source inverters (CSI), power factor correction (PFC) rectifiers, and active power filters (APF) among others. This converter can operate using both a bipolar technique and a unipolar technique. The bipolar technique switches both arms of the bridge at high frequency while the unipolar technique switches an arm at high frequency and the other one at low frequency. The unipolar technique is preferred because of two features: a) it has lower switching losses; and, b) its application requires the use of smaller filtering components. However, the control circuit of a bipolar commutated full-bridge has less complexity; hence, we focus this preliminary work in this approach. The full-bridge topology can be operating with either a pulse width modulator (PWM) or a hysteresis comparator. However, a SPWM technique is employed by comparing the sinusoidal wave (reference wave) with the triangular wave (carrier wave).

Fig. 3. Full-bridge inverter and control scheme

In this technique sine waves and a triangular carrier wave are used to generate PWM signal. The frequency of these sinusoidal waves is chosen based on the required inverter output frequency 50 Hz. The carrier triangular wave is usually a high frequency (in KHz) wave. The switching signal is generated by comparing the sinusoidal waves with the triangular wave. The comparator gives out a pulse when sine voltage is greater than the triangular voltage and this pulse is used to trigger the respective inverter switches [9]. The ratio between the triangular wave and sine wave must be an integer N, the number of voltage pulses per half-cycle, such that, 2N= fc/fs.

Frequency modulation ratio (3) is defined as the ratio of carrier frequency to the reference frequency. eq.(7).

,3 .( .) (7) Where, .(- Carrier frequency Hz, .- Reference

frequency in Hz. Amplitude modulation ratio is defined as the ratio of

amplitude of reference wave to amplitude of carrier wave. eq.(9).

34 ! !() (8) Where, !=Amplitude of reference wave, !(=Amplitude

of carrier wave.

For synchronous PWM, 3 should be an integer. The reason for using this type of PWM is asynchronous PWM results in sub harmonics that are undesirable. It can be avoided by choosing3 457. 8. , 15 3, hence there will be 45 sinusoidal modulated pulses in one complete cycle.

So to get3 45, the carrier frequency .( would be2250 C)">D (9) The outputs of an inverter contain large amount of

harmonics content. This harmonic attenuation can be achieved by several methods such as by resonating the load, by an LC filter, pulse width modulation, sine wave synthesis, selected harmonic reduction and by poly-phase inverters. Moreover in PWM technique, if the carrier frequency is increased, the harmonics components are reduced. A well designed filter can attenuate switching frequency components but impacts on control band width and the impedance presented to grid distortion []. RC &LC filters are the most used passive filters. They are divided into 1st order, 2nd Order & 3rd order filters according to the combination of the passive components [10]. LC is a 2nd order filter and eq.(10).

.E "F (10)

V. SIMULATION RESULTS In order to evaluate the above presented control scheme

and verify the analytical procedures, simulation done in PSIM scheme shown in Fig. 4, which contains the cascaded connection of the DC-DC and DC-AC stages tied to a power source. The corresponding parameters are shown in table I.

Table 1 SIMULATION PARAMETERS

Quadratic Boost Converter Full Bridge Inverter Design Parameter Value Design Parameter Value

Nominal power 300W Nominal power 300W

Input Voltage 30V Input voltage 400V

Output Voltage 400V Inverter voltage 230V

Inductor L1 600H Inverter frequency 50Hz

Inductor L2 10mH Modulation frequency

2250Hz

Capacitor C1 50F LC filter value 2mH, 20uF

Capacitor C2 100F

Kp constant 1

Ki constant 0.02

Hysteresis band 0.5

Table 2 SOLAR PANEL PARAMETERS Design parameter value

Number of cells ns 54

Maximum power pmax 215

Voltage at pmax 26.6

Current at pmax 8.09

Open-circuit voltage voc 33.2

Short-circuit current isc 8.78

Temperature coeff. Of voc -0.36

Temperature coeff. Of isc 0.06

Sd light intensity s0 1000

Sd temperature tref 25

No of panel in parallel 02

Fig. 4. Schematic diagram of PSIM simulation of the overall micro-inverter system

Fig. 5. Quadratic boost Converter Input and Output Voltage waveform

Fig. 6. Inductor Current IL1 Waveform

Fig. 7. Inverter Voltage Waveform Vac

Fig. 8. Inverter Voltage Waveform Vac(Expanded scale)

Fig. 9. Load current Waveform Iac(Expanded scale)

Fig. 10. Detail of the hysteresis band on sliding-mode surfaces

Fig. 11. Detail of the SPWM generation.

A. Input voltage disturbances The systems starts-up at 0 s with an input voltage of 15 V and reaches the steady-state. However, it is worth to point out that in real operation with a PV module, the power reference and the input voltage changes simultaneously as shown in Fig. 5.

B. Start-up condition As shown in Fig. 5,6,7, simulation results of the proposed micro-inverter reveal two main aspects. Firstly, a poor output current tracking is observable when the DC voltage is reaching its steady-state value. Hence, it is possible to assert that is necessary to use a converter with the afore-mentioned high-gain with regulation in the output voltage. Further, a minimum overshoot is observed in the input current and even more in the DC voltage. This fact is mainly due to the selected values of the Kp and Ki constants of the outer loop in the DC-DC converter, which control the resultant sliding-mode of the

inner control loop and significantly change the overall behavior dynamic.

C. Sliding-mode controllers operation and SPWM Generation

As shown in Fig. 10, two hysteresis comparators have been involved in the control scheme. Each one corresponds to the sliding-mode approach of the control of the DC-DC and DC-AC stage respectively. The simulation captures in figure 8 depict the hysteresis band of the states involved in the sliding surfaces of each converter. It is possible to observe the constraint of the currents in the hysteresis band defined around its equilibrium points. It is worth mentioning that the input current shows a sinusoidal low frequency ripple due to the DC-AC conversion. Fig. 11. is the details about the SPWM pluses for full bridge inverter.

D. System Efficiency Simulation Results shows that the Quadratic boost converter cascaded with full bridge inverter for micro-inverter system has an efficiency of 88%. Power absorbing by the panel is 280 W and power feeding to the load through full bridge inverter is 250 W. The total harmonic distortion is 2.8%

III. CONCLUSIONS The application of the sliding mode control in a dual-stage micro-inverter has been explained in this preliminary work. A PI-based sliding surface has been proposed and successfully used in the control of a quadratic boost converter in the DC-DC stage which feeds full-bridge inverter as load. The control of this inverter has been also proposed using the SPWM technique. In both cases simulation results has a reliable operation. However, it is clear that the use of the hysteresis comparators in these applications reduces the complexity of the sliding-mode implementation avoiding the chattering and modulator saturation. To summarize, this work explains the compatibility between the quadratic boost converter and the bipolar full-bridge inverter operating together as a Micro-inverter when sliding mode based controller and SPWM technique are used in DC-DC and DC-AC stages. Future work will be focused in the overall analysis including the MPPT block and grid intergation.

REFERENCES [1] O. Lopez-Santos, L. Martinez-Salamero, G. Garcia, H. Valderrama-

Blavi. Sliding-mode control of a transformer-less dual-stage grid-connected photovoltaic micro-inverter. 2013 10th International Multi-Conference on Systems, Signals & Devices (SSD) Hammamet, Tunisia, March 18-21, 2013.

[2] O. Lopez-Santos, L. Martinez-Salamero, G. Garcia, H. Valderrama-Blavi, D. Mercury. Efficiency analysis of a Sliding-mode Controlled Quadratic Boost Converter. IET Power Electronics. 2013.

[3] H. El Fadil, F. Giri. Reducing chattering phenomenon in Sliding-Mode Control of Buck-Boost Power Converters. IEEE International Symposium on Industrial Electronics (ISIE). 2008. pp. 287-292.

[4] Cortes, J. Alvarez. Robust sliding mode control for the boost converter. Technical Proceedings of the VIII IEEE International Power Electronics Congress (CIEP). 2002. pp. 208- 212.

[5] M.G. Ortiz-Lopez, J. Leyva-Ramos, E.E. Carbajal-Gutierrez, J.A. Morales-Salda na. Modelling and analysis of switch-mode cascade con-verters with a single active switch. IET Power Electronics, Vol. 1. No. 4. 2008. pp.478-487.

[6] Siew-Chong Tan Yuk-Ming Lai Chi Kong Tse Sliding Mode Control of Switching Power Converters, CRC Press.

[7] O. Lopez-Santos, L. Martinez-Salamero, G. Garcia, H. Valderrama-Blavi. Sliding-Mode Indirect Control of the Quadratic Boost Converter Operat-ing in Continuous Conduction Mode or Discontinuous Conduction Mode. IEEE 4th Colombian Workshop on Circuits and Systems (CWCAS). 2012.

[8] O. Lopez-Santos, G. Garcia, L. Martinez-Salamero. Output Voltage Reg-ulation in a Quadratic Boost Converter by Using a Multi-loop Controller Based on Sliding-Mode Control. Congres des Doctorants EDSYS, 2013.

[9] Muhammad H. Rashid, Power electronics: circuits, devices, and applications, 3rd Ed., 2004, Pearson/Prentice Hall.

[10] Nazmul Islam Raju, Md. Shahinur Islam. Study of SPWM Technique & Simulation of Designed Analog Circuit (Op-Amp) Controlled Three Phase PWM Inverter with Harmonic Reduction. 978-1-4799-0400-6/13/2013 IEEE.